RLQ analysis

Prepare data

When preparing palm traits for analysis, I had to remove several variables that contained NAs for our palm species. Also, I removed the descriptive traits about the fruit, and the variable “FruitShape” because it has blank values.

Run RLQ analysis and plot data

To successfully run this, I had to remove Habitat type from our environmental variables. The problem might be the naming convention. Sarah, can you make three letter codes for these?

That’s unreadable, plotting as seperate.

Summary of RLQ analysis. How to interpret this?

## RLQ analysis
## 
## Class: rlq dudi
## Call: rlq(dudiR = acpR.aravo, dudiL = afcL.aravo, dudiQ = acpQ.aravo, 
##     scannf = FALSE)
## 
## Total inertia: 0.657
## 
## Eigenvalues:
##      Ax1      Ax2      Ax3      Ax4      Ax5 
## 0.300155 0.228303 0.083533 0.041707 0.001744 
## 
## Projected inertia (%):
##     Ax1     Ax2     Ax3     Ax4     Ax5 
## 45.6877 34.7508 12.7148  6.3484  0.2654 
## 
## Cumulative projected inertia (%):
##     Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
##   45.69   80.44   93.15   99.50   99.77 
## 
## (Only 5 dimensions (out of 9) are shown)
## 
## 
## Eigenvalues decomposition:
##         eig     covar      sdR      sdQ      corr
## 1 0.3001551 0.5478641 1.034229 1.481707 0.3575146
## 2 0.2283026 0.4778102 1.084627 2.004471 0.2197734
## 
## Inertia & coinertia R (acpR.aravo):
##     inertia      max     ratio
## 1  1.069629 1.755539 0.6092881
## 12 2.246045 3.085130 0.7280229
## 
## Inertia & coinertia Q (acpQ.aravo):
##     inertia      max     ratio
## 1  2.195457 5.095305 0.4308784
## 12 6.213361 7.950625 0.7814933
## 
## Correlation L (afcL.aravo):
##        corr       max     ratio
## 1 0.3575146 0.9327084 0.3833080
## 2 0.2197734 0.8335977 0.2636445

Fourth-corner analysis

From tutorial: “Fourth-corner analysis can be used to test the associations between individual traits and environmental variables. To obtain a test with a correct type I error, results of model 2 (permutation of sites, i.e. rows) and 4 (permutation of species, i.e. columns) should be combined.”

 nrepet <- 999
 four.comb.aravo <- fourthcorner(p_env[,-10], p_species,
     p_traits, modeltype = 6, p.adjust.method.G = "none",
     p.adjust.method.D = "none", nrepet = nrepet)

Plotting the data: “Blue cells correspond to negative significant relationships while red cells correspond to positive significant relationships (this can be modified using the argument col).”

I used the D2 option when plotting, but others exist: stat=“D2”: the association is measured between the quantitative variable and each category separately. A correlation coefficient is used to indicate the strength of the association between the given category and the small or large values of the quantitative variable. stat=“G”: the association between the quantitative variable and the whole categorical variable is measured by a global statistic (F). stat=“D”: the association is estimated between the quantitative variable and each category separately by a measure of the within-group homogeneity. The strength of the association is indicated by the dispersion of the values of the quantitative variable for a given category.

To replot the data for multiple comparisons: “Now, we adjust p-values for multiple comparisons (here we used the fdr method using the p.adjust.4thcorner function).”

Combine both approaches

“First, a multivariate test can be applied to evaluate the global significance of the traits-environment relationships. This test is based on the total inertia of the RLQ analysis”

## class: krandtest lightkrandtest 
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6)
## 
## Number of tests:   2 
## 
## Adjustment method for multiple comparisons:   none 
## Permutation number:   999 
##      Test       Obs    Std.Obs   Alter Pvalue
## 1 Model 2 0.6569709 -0.1346780 greater  0.507
## 2 Model 4 0.6569709 -0.9536772 greater  0.829

The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:

Srlq <- fourthcorner2(p_env[,-10], p_species, p_traits,
     modeltype = 6, p.adjust.method.G = "fdr", nrepet = nrepet)
Srlq$trRLQ
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_env[, -10], tabL = p_species, tabQ = p_traits, 
##     modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
## 
## Observation: -8990.343 
## 
## Based on 999 replicates
## Simulated p-value: 0.822 
## Alternative hypothesis: greater 
## 
##       Std.Obs   Expectation      Variance 
## -9.206018e-01 -8.990088e+03  7.649906e-02

“Both approaches can be combined if RLQ scores are used to represent traits and environmental variables on a biplot. Then, significant associations revealed by the fourthcorner approach can be represented using segments (blue lines for negative associations, red lines for positive associations, see the argument col). Only traits and environmental variables that have at least one significant association are represented. Here, we apply this method using adjusted pvalues for multiple comparisons and a significant level α = 0.05.”

“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”

RLQ axes and traits

## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6,      typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                             Test   Stat         Obs     Std.Obs     Alter
## 1                AxcR1 / Climb.0 Homog.  0.96134310  2.20116058      less
## 2                AxcR2 / Climb.0 Homog.  0.89121986 -0.53679743      less
## 3                AxcR1 / Climb.1 Homog.  0.03686797 -0.24848563      less
## 4                AxcR2 / Climb.1 Homog.  0.10785496  1.78642185      less
## 5                AxcR1 / Acaul.0 Homog.  1.00000000        <NA>      less
## 6                AxcR2 / Acaul.0 Homog.  1.00000000        <NA>      less
## 7                AxcR1 / Erect.0 Homog.  0.03686797 -0.24848563      less
## 8                AxcR2 / Erect.0 Homog.  0.10785496  1.78642185      less
## 9                AxcR1 / Erect.1 Homog.  0.96134310  2.20116058      less
## 10               AxcR2 / Erect.1 Homog.  0.89121986 -0.53679743      less
## 11               AxcR1 / StemS.0 Homog.  0.03698011 -0.82249690      less
## 12               AxcR2 / StemS.0 Homog.  0.10811460  1.69818917      less
## 13               AxcR1 / StemS.1 Homog.  0.48052421 -0.47715061      less
## 14               AxcR2 / StemS.1 Homog.  0.59926258  0.29260277      less
## 15               AxcR1 / StemS.2 Homog.  0.41908006  3.49481660      less
## 16               AxcR2 / StemS.2 Homog.  0.27599200  0.82078570      less
## 17               AxcR1 / StemA.0 Homog.  0.76595294  1.53669110      less
## 18               AxcR2 / StemA.0 Homog.  0.63295693 -1.43746503      less
## 19               AxcR1 / StemA.1 Homog.  0.20361638  0.26186245      less
## 20               AxcR2 / StemA.1 Homog.  0.32299828  0.83189141      less
## 21               AxcR1 / Leave.0 Homog.  0.72348658  2.13924819      less
## 22               AxcR2 / Leave.0 Homog.  0.52504761 -1.56755644      less
## 23               AxcR1 / Leave.1 Homog.  0.24149577  0.02111477      less
## 24               AxcR2 / Leave.1 Homog.  0.44244854  1.66729070      less
## 25       AxcR1 / MaxStemHeight_m      r  0.09149172  0.68994881 two-sided
## 26       AxcR2 / MaxStemHeight_m      r -0.14448147 -1.18998713 two-sided
## 27         AxcR1 / MaxStemDia_cm      r  0.08749172  0.67358979 two-sided
## 28         AxcR2 / MaxStemDia_cm      r -0.12934431 -1.06921687 two-sided
## 29          AxcR1 / Under.canopy Homog.  0.97761339  1.77069366      less
## 30          AxcR2 / Under.canopy Homog.  0.96901013  0.58548969      less
## 31     AxcR1 / Under.understorey Homog.  0.02065195 -0.45299627      less
## 32     AxcR2 / Under.understorey Homog.  0.03098774 -0.29627554      less
## 33 AxcR1 / AverageFruitLength_cm      r  0.24503760  1.89727497 two-sided
## 34 AxcR2 / AverageFruitLength_cm      r -0.12292261 -0.96520838 two-sided
## 35           AxcR1 / Fruit.large Homog.  0.42030052  2.10914139      less
## 36           AxcR2 / Fruit.large Homog.  0.51860246  2.78553943      less
## 37           AxcR1 / Fruit.small Homog.  0.55423824  2.73768704      less
## 38           AxcR2 / Fruit.small Homog.  0.46746559  1.25826119      less
## 39     AxcR1 / Consp.conspicuous Homog.  0.28302363 -1.35476992      less
## 40     AxcR2 / Consp.conspicuous Homog.  0.49950186  1.79562903      less
## 41         AxcR1 / Consp.cryptic Homog.  0.67206694  1.88678666      less
## 42         AxcR2 / Consp.cryptic Homog.  0.46811068 -0.15736019      less
##    Pvalue Pvalue.adj  
## 1   0.996          1  
## 2   0.261  0.8150625  
## 3    0.61  0.8150625  
## 4   0.946          1  
## 5       1          1  
## 6       1          1  
## 7    0.61  0.8150625  
## 8   0.946          1  
## 9   0.996          1  
## 10  0.261  0.8150625  
## 11  0.241  0.8150625  
## 12  0.942          1  
## 13  0.308  0.8150625  
## 14  0.584  0.8150625  
## 15  0.993          1  
## 16  0.833          1  
## 17  0.929          1  
## 18  0.099      0.693  
## 19  0.594  0.8150625  
## 20  0.811          1  
## 21  0.967          1  
## 22   0.07     0.6216  
## 23  0.538  0.8150625  
## 24  0.966          1  
## 25  0.527  0.8150625  
## 26  0.264  0.8150625  
## 27  0.524  0.8150625  
## 28  0.296  0.8150625  
## 29  0.973          1  
## 30  0.713          1  
## 31  0.504  0.8150625  
## 32  0.571  0.8150625  
## 33  0.046     0.6216  
## 34  0.366  0.8150625  
## 35  0.973          1  
## 36  0.993          1  
## 37  0.988          1  
## 38  0.911          1  
## 39  0.074     0.6216  
## 40  0.976          1  
## 41  0.944          1  
## 42  0.429  0.8150625  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

RLQ axes and environmental variables

## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6,      typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                          Test Stat          Obs     Std.Obs     Alter Pvalue
## 1        Canopy.Cover / AxcQ1    r -0.012420893 -0.08504096 two-sided  0.891
## 2  Understory.Density / AxcQ1    r -0.029892325 -0.28535590 two-sided  0.784
## 3         Leaf.Litter / AxcQ1    r  0.083803687  0.83347452 two-sided  0.432
## 4       Soil.Moisture / AxcQ1    r  0.122365689  1.10765079 two-sided  0.265
## 5                 Cec / AxcQ1    r  0.046971395  1.03900906 two-sided  0.333
## 6                 T50 / AxcQ1    r  0.009956983  0.17613818 two-sided  0.897
## 7                 T10 / AxcQ1    r  0.304644385  1.82411195 two-sided  0.079
## 8       Canopy.Height / AxcQ1    r -0.124070105 -1.03016040 two-sided  0.331
## 9           Elevation / AxcQ1    r  0.056259879  0.43232450 two-sided  0.687
## 10       Canopy.Cover / AxcQ2    r  0.014571724  0.12684783 two-sided  0.846
## 11 Understory.Density / AxcQ2    r -0.114617370 -1.15933364 two-sided   0.27
## 12        Leaf.Litter / AxcQ2    r  0.049781194  0.49259572 two-sided  0.636
## 13      Soil.Moisture / AxcQ2    r -0.068450849 -0.84961406 two-sided  0.419
## 14                Cec / AxcQ2    r  0.027732905  0.71951008 two-sided  0.499
## 15                T50 / AxcQ2    r  0.098808237  1.14865071 two-sided  0.219
## 16                T10 / AxcQ2    r -0.062682617 -0.36973774 two-sided  0.699
## 17      Canopy.Height / AxcQ2    r -0.090071839 -0.81666971 two-sided   0.48
## 18          Elevation / AxcQ2    r  0.117191890  0.95719518 two-sided  0.367
##           Pvalue.adj  
## 1              0.891  
## 2              0.882  
## 3  0.816545454545455  
## 4  0.777857142857143  
## 5  0.816545454545455  
## 6              0.897  
## 7              0.708  
## 8  0.816545454545455  
## 9  0.834352941176471  
## 10             0.891  
## 11 0.777857142857143  
## 12 0.834352941176471  
## 13 0.816545454545455  
## 14 0.816545454545455  
## 15 0.777857142857143  
## 16 0.834352941176471  
## 17 0.816545454545455  
## 18 0.816545454545455  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Results can be represented using a table with colors indicating significance :

Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)

RLQ/4th corner run 2 : Splitting all lifestage and points with some forest cover

Run RLQ/ FQ analysis for all lifestage types

That’s unreadable, plotting as separate.

## [1] "RLQ for juveniles"

## [1] "RLQ for adults"

Summary of RLQ analysis. How to interpret this?

## RLQ analysis
## 
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
## 
## Total inertia: 1.429
## 
## Eigenvalues:
##      Ax1      Ax2      Ax3      Ax4      Ax5 
## 0.746537 0.500895 0.121014 0.054025 0.003262 
## 
## Projected inertia (%):
##     Ax1     Ax2     Ax3     Ax4     Ax5 
## 52.2481 35.0563  8.4695  3.7811  0.2283 
## 
## Cumulative projected inertia (%):
##     Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
##   52.25   87.30   95.77   99.55   99.78 
## 
## (Only 5 dimensions (out of 9) are shown)
## 
## 
## Eigenvalues decomposition:
##         eig     covar      sdR      sdQ      corr
## 1 0.7465371 0.8640238 1.170836 1.785317 0.4133466
## 2 0.5008948 0.7077392 1.244773 1.691688 0.3360957
## 
## Inertia & coinertia R (Rjuv):
##     inertia      max     ratio
## 1  1.370856 1.858611 0.7375703
## 12 2.920316 3.464436 0.8429412
## 
## Inertia & coinertia Q (Qjuv):
##     inertia      max     ratio
## 1  3.187357 5.160919 0.6175949
## 12 6.049164 7.993775 0.7567344
## 
## Correlation L (Ljuv):
##        corr       max     ratio
## 1 0.4133466 0.9448971 0.4374514
## 2 0.3360957 0.9087471 0.3698452
## RLQ analysis
## 
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
## 
## Total inertia: 1.04
## 
## Eigenvalues:
##      Ax1      Ax2      Ax3      Ax4      Ax5 
## 0.564979 0.338546 0.115397 0.015354 0.003838 
## 
## Projected inertia (%):
##     Ax1     Ax2     Ax3     Ax4     Ax5 
##  54.314  32.546  11.094   1.476   0.369 
## 
## Cumulative projected inertia (%):
##     Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
##   54.31   86.86   97.95   99.43   99.80 
## 
## (Only 5 dimensions (out of 10) are shown)
## 
## 
## Eigenvalues decomposition:
##         eig     covar      sdR      sdQ      corr
## 1 0.5649794 0.7516511 1.317944 1.702729 0.3349451
## 2 0.3385457 0.5818468 1.128801 2.171484 0.2373747
## 
## Inertia & coinertia R (Radu):
##     inertia      max     ratio
## 1  1.736977 2.095715 0.8288231
## 12 3.011170 3.680365 0.8181714
## 
## Inertia & coinertia Q (Qadu):
##     inertia      max     ratio
## 1  2.899287 4.937157 0.5872382
## 12 7.614631 7.890549 0.9650318
## 
## Correlation L (Ladu):
##        corr       max     ratio
## 1 0.3349451 1.0000000 0.3349451
## 2 0.2373747 0.9128287 0.2600430

Fourth-corner analysis

## [1] "FQ for juveniles"

## [1] "FQ for adults"

With adjusted p-values

## [1] "FQ for Juveniles"
## [1] "FQ for Adults"

Combine both approaches

## class: krandtest lightkrandtest 
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
## 
## Number of tests:   2 
## 
## Adjustment method for multiple comparisons:   none 
## Permutation number:   999 
##      Test     Obs    Std.Obs   Alter Pvalue
## 1 Model 2 1.42883  0.1299938 greater  0.373
## 2 Model 4 1.42883 -0.2833431 greater  0.569

## class: krandtest lightkrandtest 
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
## 
## Number of tests:   2 
## 
## Adjustment method for multiple comparisons:   none 
## Permutation number:   999 
##      Test      Obs    Std.Obs   Alter Pvalue
## 1 Model 2 1.040218 14.1026397 greater  0.001
## 2 Model 4 1.040218 -0.1732769 greater  0.549

The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:

## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER, tabL = p_speciesJUV, tabQ = p_traits, 
##     modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
## 
## Observation: -8989.571 
## 
## Based on 848 replicates
## Simulated p-value: 0.5206125 
## Alternative hypothesis: greater 
## 
##       Std.Obs   Expectation      Variance 
##  3.635986e-01 -1.067521e+04  2.149238e+07
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER, tabL = p_speciesADU, tabQ = p_traits, 
##     modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
## 
## Observation: -8989.96 
## 
## Based on 999 replicates
## Simulated p-value: 0.469 
## Alternative hypothesis: greater 
## 
##       Std.Obs   Expectation      Variance 
##  3.555372e-01 -1.065493e+04  2.193028e+07
## [1] "juvenile"

## [1] "adult"

“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”

RLQ axes and traits

## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6,      typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                             Test   Stat          Obs     Std.Obs     Alter
## 1                AxcR1 / Climb.0 Homog.  0.935408906  0.96730878      less
## 2                AxcR2 / Climb.0 Homog.  0.896219686 -0.46788626      less
## 3                AxcR1 / Climb.1 Homog.  0.062673284  0.07444970      less
## 4                AxcR2 / Climb.1 Homog.  0.100874152  0.87771669      less
## 5                AxcR1 / Acaul.0 Homog.  1.000000000        <NA>      less
## 6                AxcR2 / Acaul.0 Homog.  1.000000000        <NA>      less
## 7                AxcR1 / Erect.0 Homog.  0.062673284  0.07444970      less
## 8                AxcR2 / Erect.0 Homog.  0.100874152  0.87771669      less
## 9                AxcR1 / Erect.1 Homog.  0.935408906  0.96730878      less
## 10               AxcR2 / Erect.1 Homog.  0.896219686 -0.46788626      less
## 11               AxcR1 / StemS.0 Homog.  0.062673284 -0.42172090      less
## 12               AxcR2 / StemS.0 Homog.  0.100874152  0.87771669      less
## 13               AxcR1 / StemS.1 Homog.  0.434638318 -0.66069204      less
## 14               AxcR2 / StemS.1 Homog.  0.515663169 -0.21398743      less
## 15               AxcR1 / StemS.2 Homog.  0.336057240  1.95516021      less
## 16               AxcR2 / StemS.2 Homog.  0.379436083  2.91532672      less
## 17               AxcR1 / StemA.0 Homog.  0.823478093  2.21574440      less
## 18               AxcR2 / StemA.0 Homog.  0.594579406 -1.47389245      less
## 19               AxcR1 / StemA.1 Homog.  0.174538043  0.04400098      less
## 20               AxcR2 / StemA.1 Homog.  0.280158884  0.47985122      less
## 21               AxcR1 / Leave.0 Homog.  0.758100818  2.24583807      less
## 22               AxcR2 / Leave.0 Homog.  0.493674666 -1.56170756      less
## 23               AxcR1 / Leave.1 Homog.  0.237514667  0.04512235      less
## 24               AxcR2 / Leave.1 Homog.  0.419778917  1.50727468      less
## 25       AxcR1 / MaxStemHeight_m      r -0.210341823 -1.33485794 two-sided
## 26       AxcR2 / MaxStemHeight_m      r -0.077264855 -0.60188406 two-sided
## 27         AxcR1 / MaxStemDia_cm      r -0.214542329 -1.34534367 two-sided
## 28         AxcR2 / MaxStemDia_cm      r -0.059720466 -0.50256913 two-sided
## 29          AxcR1 / Under.canopy Homog.  0.980841113  0.92303525      less
## 30          AxcR2 / Under.canopy Homog.  0.982255001  1.08882504      less
## 31     AxcR1 / Under.understorey Homog.  0.017971110 -0.50703885      less
## 32     AxcR2 / Under.understorey Homog.  0.017628019 -0.52176153      less
## 33 AxcR1 / AverageFruitLength_cm      r -0.411890001 -2.72154411 two-sided
## 34 AxcR2 / AverageFruitLength_cm      r -0.004254722 -0.05040763 two-sided
## 35           AxcR1 / Fruit.large Homog.  0.384995644  1.64637176      less
## 36           AxcR2 / Fruit.large Homog.  0.464108800  2.20963518      less
## 37           AxcR1 / Fruit.small Homog.  0.515842044  2.27569208      less
## 38           AxcR2 / Fruit.small Homog.  0.534845101  2.63988352      less
## 39     AxcR1 / Consp.conspicuous Homog.  0.273692963 -1.14915964      less
## 40     AxcR2 / Consp.conspicuous Homog.  0.460961375  1.47668390      less
## 41         AxcR1 / Consp.cryptic Homog.  0.718840507  2.13546153      less
## 42         AxcR2 / Consp.cryptic Homog.  0.448132549 -0.23765943      less
##               Pvalue        Pvalue.adj  
## 1              0.834                 1  
## 2              0.239 0.939555555555556  
## 3  0.729545454545454 0.953181818181818  
## 4              0.816                 1  
## 5                  1                 1  
## 6                  1                 1  
## 7  0.729545454545454 0.953181818181818  
## 8              0.816                 1  
## 9              0.834                 1  
## 10             0.239 0.939555555555556  
## 11  0.48991935483871 0.939555555555556  
## 12             0.816                 1  
## 13              0.29 0.939555555555556  
## 14             0.435 0.939555555555556  
## 15              0.94                 1  
## 16             0.982                 1  
## 17             0.984                 1  
## 18             0.088            0.7476  
## 19             0.573 0.939555555555556  
## 20             0.672                 1  
## 21             0.976                 1  
## 22             0.089            0.7476  
## 23              0.54 0.939555555555556  
## 24             0.951                 1  
## 25               0.2 0.939555555555556  
## 26             0.577                 1  
## 27             0.198 0.939555555555556  
## 28             0.664                 1  
## 29             0.817                 1  
## 30             0.867                 1  
## 31 0.500576701268743 0.939555555555556  
## 32 0.567474048442907 0.939555555555556  
## 33             0.001             0.042 *
## 34             0.967                 1  
## 35             0.944                 1  
## 36             0.976                 1  
## 37             0.967                 1  
## 38             0.985                 1  
## 39             0.136 0.939555555555556  
## 40             0.953                 1  
## 41              0.97                 1  
## 42             0.424 0.939555555555556  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6,      typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                             Test   Stat          Obs     Std.Obs     Alter
## 1                AxcR1 / Climb.0 Homog.  0.836672753 -1.25688155      less
## 2                AxcR2 / Climb.0 Homog.  0.940072279  0.35896830      less
## 3                AxcR1 / Climb.1 Homog.  0.074800140  0.75299442      less
## 4                AxcR2 / Climb.1 Homog.  0.056918191 -0.05118715      less
## 5                AxcR1 / Acaul.0 Homog.  1.000000000        <NA>      less
## 6                AxcR2 / Acaul.0 Homog.  1.000000000        <NA>      less
## 7                AxcR1 / Erect.0 Homog.  0.074800140  0.75299442      less
## 8                AxcR2 / Erect.0 Homog.  0.056918191 -0.05118715      less
## 9                AxcR1 / Erect.1 Homog.  0.836672753 -1.25688155      less
## 10               AxcR2 / Erect.1 Homog.  0.940072279  0.35896830      less
## 11               AxcR1 / StemS.0 Homog.  0.100179857  2.12995286      less
## 12               AxcR2 / StemS.0 Homog.  0.061059378 -0.48373717      less
## 13               AxcR1 / StemS.1 Homog.  0.641005501  0.57497054      less
## 14               AxcR2 / StemS.1 Homog.  0.722324576  1.17791479      less
## 15               AxcR1 / StemS.2 Homog.  0.155320246 -0.92942985      less
## 16               AxcR2 / StemS.2 Homog.  0.193553765 -0.63288592      less
## 17               AxcR1 / StemA.0 Homog.  0.656649208  1.80265637      less
## 18               AxcR2 / StemA.0 Homog.  0.629379796  0.73860010      less
## 19               AxcR1 / StemA.1 Homog.  0.312689117  1.17801079      less
## 20               AxcR2 / StemA.1 Homog.  0.363941396  1.34293539      less
## 21               AxcR1 / Leave.0 Homog.  0.510919122 -1.69942334      less
## 22               AxcR2 / Leave.0 Homog.  0.566988117  0.85126100      less
## 23               AxcR1 / Leave.1 Homog.  0.488493502  1.01718767      less
## 24               AxcR2 / Leave.1 Homog.  0.421492370  1.17374967      less
## 25       AxcR1 / MaxStemHeight_m      r  0.088990901  0.55193677 two-sided
## 26       AxcR2 / MaxStemHeight_m      r  0.252057476  2.13834988 two-sided
## 27         AxcR1 / MaxStemDia_cm      r -0.035464815 -0.25817726 two-sided
## 28         AxcR2 / MaxStemDia_cm      r  0.258239812  2.20446456 two-sided
## 29          AxcR1 / Under.canopy Homog.  0.940406773  0.47747322      less
## 30          AxcR2 / Under.canopy Homog.  0.949032509  1.00781417      less
## 31     AxcR1 / Under.understorey Homog.  0.058403035  0.07372075      less
## 32     AxcR2 / Under.understorey Homog.  0.049026243 -0.16777458      less
## 33 AxcR1 / AverageFruitLength_cm      r -0.004633307 -0.16778394 two-sided
## 34 AxcR2 / AverageFruitLength_cm      r  0.158137536  1.37845374 two-sided
## 35           AxcR1 / Fruit.large Homog.  0.463222263  2.50854387      less
## 36           AxcR2 / Fruit.large Homog.  0.558166806  0.48794982      less
## 37           AxcR1 / Fruit.small Homog.  0.534548704  2.61819964      less
## 38           AxcR2 / Fruit.small Homog.  0.400441438 -1.69145817      less
## 39     AxcR1 / Consp.conspicuous Homog.  0.559426785  1.05934370      less
## 40     AxcR2 / Consp.conspicuous Homog.  0.506219974  0.04933554      less
## 41         AxcR1 / Consp.cryptic Homog.  0.439722847 -0.26063794      less
## 42         AxcR2 / Consp.cryptic Homog.  0.473926570 -0.05589842      less
##               Pvalue        Pvalue.adj  
## 1              0.127             0.654  
## 2              0.598             0.966  
## 3              0.791                 1  
## 4  0.793397231096912                 1  
## 5                  1                 1  
## 6                  1                 1  
## 7              0.791                 1  
## 8  0.793397231096912                 1  
## 9              0.127             0.654  
## 10             0.598             0.966  
## 11             0.974                 1  
## 12             0.495                 1  
## 13             0.681                 1  
## 14             0.881                 1  
## 15             0.218             0.654  
## 16             0.345          0.905625  
## 17             0.966                 1  
## 18              0.77                 1  
## 19             0.854                 1  
## 20             0.881                 1  
## 21             0.056            0.4704  
## 22             0.802                 1  
## 23             0.842                 1  
## 24             0.887                 1  
## 25             0.631                 1  
## 26             0.004             0.084 .
## 27             0.791                 1  
## 28             0.002             0.084 .
## 29             0.664                 1  
## 30              0.84                 1  
## 31 0.647497337593184                 1  
## 32 0.647497337593184                 1  
## 33             0.868                 1  
## 34             0.197             0.654  
## 35             0.981                 1  
## 36             0.688                 1  
## 37             0.996                 1  
## 38             0.043             0.168  
## 39             0.855                 1  
## 40             0.538                 1  
## 41              0.41 0.956666666666667  
## 42             0.483                 1  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

RLQ axes and environmental variables

## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6,      typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                          Test   Stat          Obs    Std.Obs     Alter Pvalue        Pvalue.adj  
## 1        Canopy.Cover / AxcQ1      r -0.023925899 -0.1934982 two-sided  0.793 0.906285714285714  
## 2  Understory.Density / AxcQ1      r -0.046616337 -0.3474136 two-sided  0.763 0.906285714285714  
## 3         Leaf.Litter / AxcQ1      r -0.004365802 -0.0126180 two-sided  0.987             0.987  
## 4       Soil.Moisture / AxcQ1      r -0.220288874 -1.6287285 two-sided   0.11 0.377142857142857  
## 5                 Cec / AxcQ1      r -0.021245562 -0.1654269 two-sided  0.739 0.906285714285714  
## 6                 T50 / AxcQ1      r  0.050329640  0.6670247 two-sided  0.555 0.830181818181818  
## 7                 T10 / AxcQ1      r -0.314893261 -1.4962719 two-sided  0.135             0.648  
## 8       Canopy.Height / AxcQ1      r  0.080491140  0.5959590 two-sided  0.586 0.830181818181818  
## 9           Elevation / AxcQ1      r  0.074152550  0.5241494 two-sided  0.629 0.838666666666667  
## 10      Habit.Primary / AxcQ1 Homog.  0.339462103 -1.5132647      less  0.087             0.522  
## 11    Habit.Secondary / AxcQ1 Homog.  0.586665219  1.2752312      less  0.886 0.924521739130435  
## 12   Habit.Transition / AxcQ1 Homog.  0.005065871 -0.3037668      less  0.434 0.801230769230769  
## 13       Canopy.Cover / AxcQ2      r -0.077862187 -1.1990435 two-sided   0.25 0.690666666666667  
## 14 Understory.Density / AxcQ2      r -0.189627260 -1.6219673 two-sided   0.11 0.377142857142857  
## 15        Leaf.Litter / AxcQ2      r  0.155590484  1.1873636 two-sided  0.259 0.690666666666667  
## 16      Soil.Moisture / AxcQ2      r -0.067983135 -0.5704121 two-sided  0.618 0.830181818181818  
## 17                Cec / AxcQ2      r  0.052327639  0.8462091 two-sided  0.423 0.801230769230769  
## 18                T50 / AxcQ2      r  0.153959525  1.5089620 two-sided  0.176 0.474666666666667  
## 19                T10 / AxcQ2      r  0.119721332  0.5934057 two-sided  0.587 0.830181818181818  
## 20      Canopy.Height / AxcQ2      r -0.132627095 -1.0155636 two-sided   0.36 0.785454545454545  
## 21          Elevation / AxcQ2      r  0.213975341  1.4183420 two-sided  0.176 0.690666666666667  
## 22      Habit.Primary / AxcQ2 Homog.  0.548269612  1.2032756      less  0.882 0.922434782608696  
## 23    Habit.Secondary / AxcQ2 Homog.  0.448034986 -0.5104000      less  0.298            0.7152  
## 24   Habit.Transition / AxcQ2 Homog.  0.003669394 -0.7159396      less  0.203 0.690666666666667  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6,      typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                          Test   Stat          Obs     Std.Obs     Alter Pvalue        Pvalue.adj  
## 1        Canopy.Cover / AxcQ1      r -0.020525343 -0.52987608 two-sided  0.593 0.884210526315789  
## 2  Understory.Density / AxcQ1      r  0.176408140  1.90263412 two-sided  0.066            0.6384  
## 3         Leaf.Litter / AxcQ1      r -0.050385708 -0.56929404 two-sided  0.642 0.884210526315789  
## 4       Soil.Moisture / AxcQ1      r -0.201383111 -1.92812765 two-sided  0.084            0.6384  
## 5                 Cec / AxcQ1      r -0.032244658 -0.69057769 two-sided  0.552 0.884210526315789  
## 6                 T50 / AxcQ1      r  0.062841701  1.54634036 two-sided  0.133            0.6384  
## 7                 T10 / AxcQ1      r  0.104356069  1.04877602 two-sided  0.335 0.884210526315789  
## 8       Canopy.Height / AxcQ1      r -0.079818074 -0.61186294 two-sided   0.53 0.884210526315789  
## 9           Elevation / AxcQ1      r  0.292632454  1.94190843 two-sided  0.061            0.6384  
## 10      Habit.Primary / AxcQ1 Homog.  0.616404905  3.82920806      less      1                 1  
## 11    Habit.Secondary / AxcQ1 Homog.  0.351213487  0.06348844      less  0.453 0.884210526315789  
## 12   Habit.Transition / AxcQ1 Homog.  0.020031880  1.01380927      less   0.89 0.970909090909091  
## 13       Canopy.Cover / AxcQ2      r -0.059842511 -1.41144181 two-sided  0.177 0.685714285714286  
## 14 Understory.Density / AxcQ2      r -0.043046543 -0.55372181 two-sided  0.589 0.884210526315789  
## 15        Leaf.Litter / AxcQ2      r  0.116980880  1.34077455 two-sided    0.2 0.685714285714286  
## 16      Soil.Moisture / AxcQ2      r -0.059469654 -0.50494174 two-sided  0.671 0.884210526315789  
## 17                Cec / AxcQ2      r  0.003349974  0.07791062 two-sided  0.949                 1  
## 18                T50 / AxcQ2      r -0.015681784 -0.42301126 two-sided    0.7 0.884210526315789  
## 19                T10 / AxcQ2      r  0.114251067  0.99929615 two-sided  0.404 0.884210526315789  
## 20      Canopy.Height / AxcQ2      r  0.185686323  1.51680403 two-sided  0.122            0.6384  
## 21          Elevation / AxcQ2      r  0.006309089  0.11471122 two-sided  0.901                 1  
## 22      Habit.Primary / AxcQ2 Homog.  0.671935150  7.51254013      less      1                 1  
## 23    Habit.Secondary / AxcQ2 Homog.  0.315497275 -0.70813760      less  0.244             0.732  
## 24   Habit.Transition / AxcQ2 Homog.  0.011255924  0.97553325      less  0.842 0.962285714285714  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Results can be represented using a table with colors indicating significance :

## [1] "juveniles"

## [1] "adults"

Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)

## [1] "juveniles"

## [1] "adults"

RLQ/4th corner run 3 : Checking to see which environmental variables may be removed and “endemism” as a trait

 p_traits$Endemic<-as.factor(palm_list$Endemic)
# splom(p_envFORCOVER)
res1 <- corrplot::cor.mtest(p_envFORCOVER[,1:9], conf.level = 0.95)
corrplot::corrplot(cor(p_envFORCOVER[,1:9]),p.mat = res1$p,type = "upper")

corrplot::corrplot(cor(p_envFORCOVER[,1:9]), p.mat = res1$p, insig = "p-value")

corrplot::corrplot(cor(p_envFORCOVER[,1:9]), p.mat = res1$p, insig = "blank")

corrplot::corrplot(cor(p_envFORCOVER[,1:9]), p.mat = res1$p, insig = "pch",pch= 1)

library("PerformanceAnalytics")
## Loading required package: xts
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## 
## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
## 
##     first, last
## 
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
## 
##     legend
chart.Correlation(p_envFORCOVER[,1:9], histogram=TRUE, pch=19)

tempdf<-NULL
tempdf$a<-seq(1,2,.1)
tempdf$b<-seq(2,3,.1)
tempdf<-as.data.frame(tempdf)
rownames(tempdf)<-LETTERS[1:11]
tempL <- dudi.coa(tempdf, scannf = FALSE)

RLQ/4th corner run 4 : Including Luke’s data and broken down by age

Run RLQ/ FQ analysis for all lifestage types COMBINED DATA

That’s unreadable, plotting as separate.

## [1] "RLQ for juveniles"

## [1] "RLQ for adults"

Summary of RLQ analysis. How to interpret this?

## RLQ analysis
## 
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
## 
## Total inertia: 0.5071
## 
## Eigenvalues:
##     Ax1     Ax2     Ax3     Ax4     Ax5 
## 0.30533 0.11443 0.06096 0.02369 0.00200 
## 
## Projected inertia (%):
##     Ax1     Ax2     Ax3     Ax4     Ax5 
## 60.2072 22.5644 12.0197  4.6722  0.3943 
## 
## Cumulative projected inertia (%):
##     Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
##   60.21   82.77   94.79   99.46   99.86 
## 
## (Only 5 dimensions (out of 8) are shown)
## 
## 
## Eigenvalues decomposition:
##         eig     covar      sdR      sdQ      corr
## 1 0.3053304 0.5525671 1.063631 1.508370 0.3444183
## 2 0.1144315 0.3382772 1.111907 1.627049 0.1869837
## 
## Inertia & coinertia R (Rjuv):
##     inertia      max     ratio
## 1  1.131310 1.408984 0.8029265
## 12 2.367647 2.673132 0.8857201
## 
## Inertia & coinertia Q (Qjuv):
##     inertia      max     ratio
## 1  2.275181 3.708939 0.6134317
## 12 4.922468 6.934943 0.7098066
## 
## Correlation L (Ljuv):
##        corr       max     ratio
## 1 0.3444183 0.8781144 0.3922248
## 2 0.1869837 0.8370330 0.2233887
## RLQ analysis
## 
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
## 
## Total inertia: 0.3568
## 
## Eigenvalues:
##      Ax1      Ax2      Ax3      Ax4      Ax5 
## 0.192475 0.086756 0.067868 0.005586 0.002817 
## 
## Projected inertia (%):
##     Ax1     Ax2     Ax3     Ax4     Ax5 
## 53.9414 24.3135 19.0201  1.5656  0.7894 
## 
## Cumulative projected inertia (%):
##     Ax1   Ax1:2   Ax1:3   Ax1:4   Ax1:5 
##   53.94   78.25   97.27   98.84   99.63 
## 
## (Only 5 dimensions (out of 8) are shown)
## 
## 
## Eigenvalues decomposition:
##          eig     covar      sdR      sdQ      corr
## 1 0.19247487 0.4387196 1.086161 1.913300 0.2111105
## 2 0.08675598 0.2945437 1.102252 1.403553 0.1903882
## 
## Inertia & coinertia R (Radu):
##     inertia      max     ratio
## 1  1.179745 1.387695 0.8501476
## 12 2.394704 2.740164 0.8739273
## 
## Inertia & coinertia Q (Qadu):
##     inertia      max     ratio
## 1  3.660716 4.077184 0.8978541
## 12 5.630678 7.312295 0.7700288
## 
## Correlation L (Ladu):
##        corr       max     ratio
## 1 0.2111105 1.0000000 0.2111105
## 2 0.1903882 0.9480088 0.2008296

Fourth-corner analysis

## [1] "FQ for juveniles"

## [1] "FQ for adults"

With adjusted p-values

## [1] "FQ for Juveniles"
## [1] "FQ for Adults"

Combine both approaches

## class: krandtest lightkrandtest 
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
## 
## Number of tests:   2 
## 
## Adjustment method for multiple comparisons:   none 
## Permutation number:   999 
##      Test      Obs   Std.Obs   Alter Pvalue
## 1 Model 2 0.507133 11.989747 greater  0.001
## 2 Model 4 0.507133  0.149111 greater  0.414

## class: krandtest lightkrandtest 
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
## 
## Number of tests:   2 
## 
## Adjustment method for multiple comparisons:   none 
## Permutation number:   999 
##      Test       Obs    Std.Obs   Alter Pvalue
## 1 Model 2 0.3568223 12.3122528 greater  0.001
## 2 Model 4 0.3568223  0.9470843 greater  0.187

The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:

## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envCombined, tabL = JuvCombined, tabQ = p_traits2, 
##     modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
## 
## Observation: 0.507133 
## 
## Based on 964 replicates
## Simulated p-value: 0.4310881 
## Alternative hypothesis: greater 
## 
##     Std.Obs Expectation    Variance 
##  0.07735429  0.49603360  0.02058880
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envCombined, tabL = AduCombined, tabQ = p_traits2, 
##     modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
## 
## Observation: 0.3568223 
## 
## Based on 999 replicates
## Simulated p-value: 0.134 
## Alternative hypothesis: greater 
## 
##       Std.Obs   Expectation      Variance 
##  5.358126e-01 -2.675706e+03  2.494404e+07
## [1] "juvenile"

## [1] "adult"

“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”

RLQ axes and traits

## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6,      typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                             Test   Stat          Obs     Std.Obs     Alter
## 1                AxcR1 / Climb.0 Homog.  0.950691650 -0.02627275      less
## 2                AxcR2 / Climb.0 Homog.  0.941841026 -0.18914483      less
## 3                AxcR1 / Climb.1 Homog.  0.033731565 -0.04376948      less
## 4                AxcR2 / Climb.1 Homog.  0.049479519  1.41768123      less
## 5                AxcR1 / Erect.0 Homog.  0.033731565 -0.04376948      less
## 6                AxcR2 / Erect.0 Homog.  0.049479519  1.41768123      less
## 7                AxcR1 / Erect.1 Homog.  0.950691650 -0.02627275      less
## 8                AxcR2 / Erect.1 Homog.  0.941841026 -0.18914483      less
## 9                AxcR1 / StemS.0 Homog.  0.042486336 -0.54922290      less
## 10               AxcR2 / StemS.0 Homog.  0.059233726  1.31869388      less
## 11               AxcR1 / StemS.1 Homog.  0.600092020  0.05313071      less
## 12               AxcR2 / StemS.1 Homog.  0.663529348  0.95674919      less
## 13               AxcR1 / StemS.2 Homog.  0.337273734  1.93148946      less
## 14               AxcR2 / StemS.2 Homog.  0.267940716 -0.24725384      less
## 15               AxcR1 / StemA.0 Homog.  0.413618760  1.00139931      less
## 16               AxcR2 / StemA.0 Homog.  0.409856391  0.51879286      less
## 17               AxcR1 / StemA.1 Homog.  0.572991793  3.46109130      less
## 18               AxcR2 / StemA.1 Homog.  0.587847629  3.72888398      less
## 19               AxcR1 / Leave.0 Homog.  0.354248320 -0.08996388      less
## 20               AxcR2 / Leave.0 Homog.  0.353383576 -0.11390124      less
## 21               AxcR1 / Leave.1 Homog.  0.616579602  3.17434276      less
## 22               AxcR2 / Leave.1 Homog.  0.646520452  3.59105969      less
## 23       AxcR1 / MaxStemHeight_m      r -0.081641368 -0.55717044 two-sided
## 24       AxcR2 / MaxStemHeight_m      r  0.019080907  0.21166716 two-sided
## 25         AxcR1 / MaxStemDia_cm      r -0.111440071 -0.75373634 two-sided
## 26         AxcR2 / MaxStemDia_cm      r  0.051767377  0.59655000 two-sided
## 27          AxcR1 / Under.canopy Homog.  0.825995793 -0.24892518      less
## 28          AxcR2 / Under.canopy Homog.  0.824299326 -0.34848379      less
## 29     AxcR1 / Under.understorey Homog.  0.131796389  0.03200571      less
## 30     AxcR2 / Under.understorey Homog.  0.173736036  0.43373567      less
## 31 AxcR1 / AverageFruitLength_cm      r  0.003639056  0.04056113 two-sided
## 32 AxcR2 / AverageFruitLength_cm      r  0.139110582  1.58693218 two-sided
## 33           AxcR1 / Fruit.large Homog.  0.171370100 -0.10348424      less
## 34           AxcR2 / Fruit.large Homog.  0.225979472  0.35982084      less
## 35           AxcR1 / Fruit.small Homog.  0.816271465  3.49025408      less
## 36           AxcR2 / Fruit.small Homog.  0.742787554 -0.61921641      less
## 37     AxcR1 / Consp.conspicuous Homog.  0.665815314  1.41237617      less
## 38     AxcR2 / Consp.conspicuous Homog.  0.699872302  1.80720472      less
## 39         AxcR1 / Consp.cryptic Homog.  0.317460710  0.88930762      less
## 40         AxcR2 / Consp.cryptic Homog.  0.298427569 -0.32309643      less
## 41               AxcR1 / Endem.N Homog.  0.722721789 -0.13586548      less
## 42               AxcR2 / Endem.N Homog.  0.720851064 -0.24067573      less
## 43               AxcR1 / Endem.Y Homog.  0.191637919 -0.40063864      less
## 44               AxcR2 / Endem.Y Homog.  0.272932571  0.56141136      less
##               Pvalue        Pvalue.adj  
## 1              0.341 0.883666666666667  
## 2               0.44 0.883666666666667  
## 3  0.710526315789474 0.883666666666667  
## 4              0.912 0.955428571428572  
## 5  0.710526315789474 0.883666666666667  
## 6              0.912 0.955428571428572  
## 7              0.341 0.883666666666667  
## 8               0.44 0.883666666666667  
## 9              0.388 0.883666666666667  
## 10             0.895 0.955428571428572  
## 11             0.517 0.883666666666667  
## 12             0.847 0.955428571428572  
## 13             0.962 0.984372093023256  
## 14             0.415 0.883666666666667  
## 15             0.848 0.955428571428572  
## 16              0.73 0.944705882352941  
## 17             0.999                 1  
## 18                 1                 1  
## 19             0.477 0.735862068965517  
## 20             0.475 0.735862068965517  
## 21             0.998                 1  
## 22                 1                 1  
## 23             0.597 0.883666666666667  
## 24             0.866                 1  
## 25             0.489 0.883666666666667  
## 26             0.578 0.883666666666667  
## 27             0.322 0.883666666666667  
## 28             0.335 0.883666666666667  
## 29             0.608 0.883666666666667  
## 30             0.684 0.883666666666667  
## 31             0.981                 1  
## 32             0.096              0.66  
## 33             0.533 0.883666666666667  
## 34             0.657 0.883666666666667  
## 35                 1                 1  
## 36             0.265 0.883666666666667  
## 37             0.904                 1  
## 38             0.961                 1  
## 39              0.83 0.955428571428572  
## 40             0.371 0.680166666666667  
## 41             0.413 0.883666666666667  
## 42             0.385 0.883666666666667  
## 43             0.384 0.883666666666667  
## 44             0.755 0.949142857142857  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6,      typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                             Test   Stat         Obs      Std.Obs     Alter
## 1                AxcR1 / Climb.0 Homog.  0.97179858  0.915771315      less
## 2                AxcR2 / Climb.0 Homog.  0.97948921  2.497885557      less
## 3                AxcR1 / Climb.1 Homog.  0.02531189 -0.368127584      less
## 4                AxcR2 / Climb.1 Homog.  0.01348188 -0.607435103      less
## 5                AxcR1 / Erect.0 Homog.  0.02531189 -0.368127584      less
## 6                AxcR2 / Erect.0 Homog.  0.01348188 -0.607435103      less
## 7                AxcR1 / Erect.1 Homog.  0.97179858  0.915771315      less
## 8                AxcR2 / Erect.1 Homog.  0.97948921  2.497885557      less
## 9                AxcR1 / StemS.0 Homog.  0.04679292 -0.468267804      less
## 10               AxcR2 / StemS.0 Homog.  0.04346445 -0.594532342      less
## 11               AxcR1 / StemS.1 Homog.  0.47268434 -0.643920189      less
## 12               AxcR2 / StemS.1 Homog.  0.53370050  2.924448317      less
## 13               AxcR1 / StemS.2 Homog.  0.46353583  0.933883756      less
## 14               AxcR2 / StemS.2 Homog.  0.41647109  0.789333538      less
## 15               AxcR1 / StemA.0 Homog.  0.21466306 -1.158529289      less
## 16               AxcR2 / StemA.0 Homog.  0.29338290  3.848765983      less
## 17               AxcR1 / StemA.1 Homog.  0.78478607  1.170086604      less
## 18               AxcR2 / StemA.1 Homog.  0.69891091  3.336111180      less
## 19               AxcR1 / Leave.0 Homog.  0.18698199 -0.838501290      less
## 20               AxcR2 / Leave.0 Homog.  0.26528813  4.425529380      less
## 21               AxcR1 / Leave.1 Homog.  0.81301791  0.884416114      less
## 22               AxcR2 / Leave.1 Homog.  0.71751015  2.874149109      less
## 23       AxcR1 / MaxStemHeight_m      r -0.11128831 -1.388747528 two-sided
## 24       AxcR2 / MaxStemHeight_m      r -0.04326206 -0.584694138 two-sided
## 25         AxcR1 / MaxStemDia_cm      r -0.16305380 -2.060055734 two-sided
## 26         AxcR2 / MaxStemDia_cm      r -0.02330345 -0.255398809 two-sided
## 27          AxcR1 / Under.canopy Homog.  0.84135842 -0.055587184      less
## 28          AxcR2 / Under.canopy Homog.  0.84882465  0.891265991      less
## 29     AxcR1 / Under.understorey Homog.  0.15371029  0.060170728      less
## 30     AxcR2 / Under.understorey Homog.  0.14529232 -0.003084907      less
## 31 AxcR1 / AverageFruitLength_cm      r -0.20867857 -2.759783910 two-sided
## 32 AxcR2 / AverageFruitLength_cm      r  0.03378664  0.533706335 two-sided
## 33           AxcR1 / Fruit.large Homog.  0.21701516  0.198949939      less
## 34           AxcR2 / Fruit.large Homog.  0.22896442  0.314627941      less
## 35           AxcR1 / Fruit.small Homog.  0.74297350 -0.435336291      less
## 36           AxcR2 / Fruit.small Homog.  0.76496435 -0.325948611      less
## 37     AxcR1 / Consp.conspicuous Homog.  0.76188172  1.400910039      less
## 38     AxcR2 / Consp.conspicuous Homog.  0.72621006  1.442229026      less
## 39         AxcR1 / Consp.cryptic Homog.  0.23058913 -0.496923851      less
## 40         AxcR2 / Consp.cryptic Homog.  0.27337586  1.876080636      less
## 41               AxcR1 / Endem.N Homog.  0.83942871  0.435476460      less
## 42               AxcR2 / Endem.N Homog.  0.85125177  1.370082319      less
## 43               AxcR1 / Endem.Y Homog.  0.15572888 -0.519435782      less
## 44               AxcR2 / Endem.Y Homog.  0.13859593 -0.740827054      less
##               Pvalue        Pvalue.adj  
## 1              0.817                 1  
## 2              0.999                 1  
## 3  0.489308176100629 0.861182389937107  
## 4  0.306918238993711 0.861182389937107  
## 5  0.489308176100629 0.861182389937107  
## 6  0.306918238993711 0.861182389937107  
## 7              0.817                 1  
## 8              0.999                 1  
## 9  0.421599169262721 0.861182389937107  
## 10 0.364485981308411 0.861182389937107  
## 11             0.317 0.861182389937107  
## 12             0.996                 1  
## 13             0.764 0.908540540540541  
## 14             0.752 0.908540540540541  
## 15             0.126 0.320222222222222  
## 16                 1                 1  
## 17             0.877                 1  
## 18                 1                 1  
## 19             0.194 0.449263157894737  
## 20                 1                 1  
## 21             0.816                 1  
## 22             0.998                 1  
## 23             0.179 0.861182389937107  
## 24             0.562 0.868645161290323  
## 25             0.031 0.227333333333333  
## 26             0.808 0.935578947368421  
## 27             0.335 0.861182389937107  
## 28             0.827                 1  
## 29             0.665 0.896342857142857  
## 30             0.612 0.868645161290323  
## 31             0.003            0.0264 *
## 32             0.606 0.868645161290323  
## 33             0.699 0.896342857142857  
## 34             0.679 0.896342857142857  
## 35             0.235 0.861182389937107  
## 36              0.32 0.861182389937107  
## 37             0.921                 1  
## 38             0.926                 1  
## 39             0.316 0.604521739130435  
## 40              0.97                 1  
## 41             0.638           0.87725  
## 42             0.929                 1  
## 43             0.397 0.861182389937107  
## 44              0.28 0.861182389937107  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

RLQ axes and environmental variables

## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6,      typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                     Test   Stat          Obs     Std.Obs     Alter Pvalue        Pvalue.adj  
## 1    Under.dense / AxcQ1 Homog.  0.221464258  0.48155493      less  0.743            0.8916  
## 2      Under.low / AxcQ1 Homog.  0.218403774 -0.96924737      less  0.155           0.34875  
## 3   Under.medium / AxcQ1 Homog.  0.550063386  1.37664121      less  0.923             0.969  
## 4            Cec / AxcQ1      r  0.042828674  1.80999341 two-sided  0.082             0.279  
## 5            T50 / AxcQ1      r -0.000714878  0.04114116 two-sided  0.974             0.974  
## 6            T10 / AxcQ1      r -0.026242242 -0.72506195 two-sided  0.472             0.783  
## 7  Canopy.Height / AxcQ1      r -0.043252066 -0.62645490 two-sided  0.566 0.727714285714286  
## 8      Elevation / AxcQ1      r  0.343316027  2.21082571 two-sided  0.012             0.126  
## 9   DIST_TO_EDGE / AxcQ1      r  0.043264696  0.64080035 two-sided  0.528 0.727714285714286  
## 10   Under.dense / AxcQ2 Homog.  0.271414040  1.96134648      less  0.951             0.974  
## 11     Under.low / AxcQ2 Homog.  0.208125884 -1.62523191      less  0.064             0.279  
## 12  Under.medium / AxcQ2 Homog.  0.513648363  0.13750044      less    0.5             0.783  
## 13           Cec / AxcQ2      r -0.043906956 -1.80675366 two-sided  0.065             0.279  
## 14           T50 / AxcQ2      r -0.017580374 -0.45199623 two-sided  0.594 0.822461538461538  
## 15           T10 / AxcQ2      r  0.024502707  0.64251079 two-sided  0.522             0.783  
## 16 Canopy.Height / AxcQ2      r  0.153488306  2.14193724 two-sided  0.014             0.126  
## 17     Elevation / AxcQ2      r  0.019284269  0.12471550 two-sided  0.932             0.974  
## 18  DIST_TO_EDGE / AxcQ2      r  0.098216141  1.70040586 two-sided  0.093             0.279  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Fourth-corner Statistics
## ------------------------
## Permutation method  Comb. 2 and 4  ( 999  permutations)
## 
## Adjustment method for multiple comparisons:   fdr 
## call:  fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6,      typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr") 
## 
## ---
## 
##                     Test   Stat          Obs     Std.Obs     Alter Pvalue        Pvalue.adj  
## 1    Under.dense / AxcQ1 Homog.  0.214360348 -0.02268301      less  0.516 0.714461538461538  
## 2      Under.low / AxcQ1 Homog.  0.306199419  1.55980056      less  0.954             0.954  
## 3   Under.medium / AxcQ1 Homog.  0.476937675 -1.27201660      less  0.105             0.378  
## 4            Cec / AxcQ1      r  0.031433924  1.66695763 two-sided  0.094             0.378  
## 5            T50 / AxcQ1      r -0.007846279 -0.20751648 two-sided  0.873 0.924352941176471  
## 6            T10 / AxcQ1      r -0.132361714 -2.07400258 two-sided  0.011             0.084 .
## 7  Canopy.Height / AxcQ1      r -0.152381058 -1.95728491 two-sided  0.014             0.084 .
## 8      Elevation / AxcQ1      r  0.084566234  1.10490431 two-sided  0.278            0.6255  
## 9   DIST_TO_EDGE / AxcQ1      r -0.033692825 -0.50940510 two-sided  0.696           0.83025  
## 10   Under.dense / AxcQ2 Homog.  0.233712304  0.60296633      less  0.741            0.8892  
## 11     Under.low / AxcQ2 Homog.  0.286539392  0.35748142      less  0.654 0.840857142857143  
## 12  Under.medium / AxcQ2 Homog.  0.476587859 -1.12584597      less   0.15              0.45  
## 13           Cec / AxcQ2      r -0.005443898 -0.20991642 two-sided  0.846 0.895764705882353  
## 14           T50 / AxcQ2      r -0.030475271 -0.95878494 two-sided  0.359            0.6462  
## 15           T10 / AxcQ2      r  0.036422985  0.59083109 two-sided  0.615           0.83025  
## 16 Canopy.Height / AxcQ2      r  0.050444774  0.69333076 two-sided  0.537           0.83025  
## 17     Elevation / AxcQ2      r  0.175774038  2.66175775 two-sided  0.005             0.084 .
## 18  DIST_TO_EDGE / AxcQ2      r  0.071782890  1.06132140 two-sided  0.356            0.6462  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Results can be represented using a table with colors indicating significance :

## [1] "juveniles"

## [1] "adults"

Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)

## [1] "juveniles"

## [1] "adults"